AJP - Regulatory, Integrative and Comparative Physiology, Vol 246, Issue 5 641-R650, Copyright © 1984 by American Physiological Society
Fitting physiological models to data
D. Garfinkel and K. A. Fegley
Methods of fitting models to experimental data obtained from biological
systems are reviewed. The Michaelis-Menten model is used as the working
example of a familiar and well-studied biological model. Criteria for
selecting models include goodness of fit, freedom from systematic errors,
and simplicity. A given model is usually fitted and the optimal parameters
determined by minimization of an objective function, usually the sum of the
squared errors. Freedom from systematic errors is best judged graphically.
The important mathematical methods of fitting models are derived from the
calculus and include linear and quadratic programming. The latter leads to
minimization of the sum of squares of errors. Optimal search procedures,
which also perform this minimization, are surveyed. Other properties of
models, such as the proper number of parameters and whether linearization
is appropriate, are discussed. The specialized problems of biological
models and data are considered.
